Research On Synchronization Control Of Fractional-order Chaotic Systems

With the breakthrough of fractional calculus theory in recent decades and the study of synchronization of integer order chaotic system,the synchronization of fractional order chaotic systems has also made gradual progress.Because of the close connection between its dynamic characteristics and the order of system,fractional order chaotic system,as the natural generalization of integer order chaotic system,has therefore more complicated chaotic characters and a wider application prospect in the chaotic field.In this thesis,we study the synchronization control of a class of fractional chaotic systems with unbalanced point and the synchronization control of fractional order chaotic systems with time delay.The main work and innovation are as follows:First of all,for the 0-1 test of fractional order chaotic systems with time delay and analysis of chaos,On the basis of the traditional model of fractional order chaotic system,the time delay control term and the time delay linear perturbation term can be added or the non-delay term can be transformed into the delay term.According to these methods,two kinds of new fractal order chaotic systems are constructed,whose chaotic state can be judged by methods such as phase diagram,attractor and 0-1 test method.There will be stability analysis of the two proposed new fractional order chaotic systems and verification that the system has been in chaotic state from the quantitative point of view.Secondly,research on synchronization control of a class of four-dimensional fractional order chaotic system without balanced point is studied;The modified calculus transformation method is used to solve the fractional order chaotic system;The 0-1 test method is used to detect the chaotic behavior of the fractional nonlinear system and chaotic behavior is distinguished by approximation of K value to asymptotic growth rate.The stability of the four-dimensional fractional order chaotic system is realized by designing the appropriate state feedback controller by the stability theory.The feasibility of this algorithm is verified by simulation.Finally,a new class of fractional order chaotic systems with time delay is proposed,and the synchronization of fractional order chaotic systems with time delay is realized by the linear feedback controller designed on the basis of the stability theory.In order to solve the problem of different structure synchronization of fractional order chaotic systems with different order,two new fractional order chaotic systems with different orders are proposed,and the effective controller is designed to realize the complete synchronization between the two systems.On the basis of the theoretical analysis of chaotic secure communication technology,a private communication method is designed out of the combination with the newly proposed fractional order chaotic system with time delay and chaos concealment technology.Besides,the validity of the scheme is proved by numerical simulation.